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math.OC2024
Non-Euclidean High-Order Smooth Convex Optimization
Juan Pablo Contreras, Cristóbal Guzmán, David Martínez-Rubio
We develop algorithms for the optimization of convex objectives that have Hölder continuous -th derivatives by using a -th order oracle, for any . Our algorithms wo…
math.OC2024
Optimization on a Finer Scale: Bounded Local Subgradient Variation Perspective
Jelena Diakonikolas, Cristóbal Guzmán
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local region…
math.OC2024
Mirror Descent Algorithms with Nearly Dimension-Independent Rates for Differentially-Private Stochastic Saddle-Point Problems
Tomás González, Cristóbal Guzmán, Courtney Paquette
We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the setting. We propose -DP algorithms based on stochast…